Forward-looking information in VAR models and the price puzzle

This 2006 Journal of Monetary Economics paper by Sophocles Brissimis and Nicholas Magginas asks whether augmenting a standard monetary VAR with forward-looking information can resolve the “price puzzle” — the counter-theoretical finding that prices rise, rather than fall, after a contractionary monetary policy shock — in a modern US sample dominated by the Greenspan Federal Reserve. Using monthly US data from January 1989 to June 2004 (the period for which federal funds futures data are available, and one the authors characterize as a homogeneous policy regime), they first show that a standard four-variable recursive (Cholesky) VAR — industrial production, CPI, a commodity price index, and the federal funds rate, with 6 lags chosen by AIC and SBC — produces “a strong counter-theoretical response of CPI to the monetary policy shock,” with CPI rising throughout all 48 months of the impulse response. They then replace this baseline with a system ordered {composite leading indicator (LCOM), industrial production, CPI, federal funds rate}, in which the one-month-ahead federal funds futures rate (FFF) — the market’s expectation of the current month’s funds rate — enters as an exogenous variable rather than as part of the endogenous ordering, so that the monetary policy shock is identified as the orthogonalized residual of the funds-rate equation. In this augmented system “the price puzzle is solved”: CPI shows only a small, statistically insignificant positive response for the first 2-3 months, then declines gradually to a trough 30 months after the shock, with the decline becoming statistically significant after 14 months; industrial production declines steadily to a trough 5-6 months out and returns to its pre-shock level roughly two years (24 months) after the shock, tracking LCOM’s response with a 1-2 month lag; and the funds-rate shock itself dies out quickly (4-5 months), so there is “no policy innovation paradox.” The result is robust to replacing FFF with an implied one-month forward rate constructed from two-month Libor and the effective funds rate, both over the same 1989-2004 window and over a longer 1986-2004 sample (the earliest for which Libor data exist), and the authors note that further extending the system to seven variables in a Christiano-Eichenbaum-Evans/Kim-style specification with total and non-borrowed reserves and M2 yields “no significant gains” in resolving the puzzle. The paper’s overall diagnosis is that the price puzzle reflects the VAR’s omission of the richer, forward-looking information set the central bank actually uses to forecast inflation and output; the federal funds futures rate and the composite leading indicator proxy for that omitted information without expanding the VAR’s dimensionality.

Sophocles N. Brissimis | Macro Paper Warehouse

Forward-looking information in VAR models and the price puzzle